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L'Hôpital's rule

transformation and compositions notes

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L'Hôpital's rule

I?. Ei- Pre-AP Algebra 2 Day 3 Notes: Transformations and Compositions Date Transformations y=?af[?b(x?c)](+c? c H &1M s C) t ( c) o &A \ \ on j. vri (G vv I I Graph and state the transformation y = f(x) to y = f(x - 3) + 2 y = 2f(x) y = f(2x) (, ::; 91 dt L j-vcLLNc I - VI aizA. pxvawc' 10 ticw ti a 0 10 y = f(x)to y = f(4x) 9 OY7.A4'iit cWrcc1 It C, 10 y=f(x) to y= ?f(x+2) y=f(?x) y=f(x) onicrt Cftc4ioj k horl SkICkI 10~ of O-i CtWi&'\ [r1 C,-& Lmi1z H- y = f(x) - 2 _& y = 2f(3x) + 3 -7-- - V ho?i\ cecA s\'\E4' b 3 o'iziA 1;S aN C_ Yify Compositon of functions: Putting one function into another. Ex. Given f(x) and gf4piS would be f(g(x))?"f of g of x'. **When

Limits

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Limits Number value that f(x) approaches as the values of x approach a specific numberIf f(x) is a polynomial or a rational function and a is in the domain of f(x), then Limits that fail to exist 1. If f(x) approaches a different number from the right than from the left: 2. If f(x) increases or decreases without bound as it approaches a number: 3. If f(x) oscillates between 2 fixed value One-sided limits If only approaching from the right If only approaching from the left Limit Existence Theorem = L iff = L = Vertical Asymptote If = or = Then x=a is a vertical asymptote Horizontal Asymptote If or Then y=b is a horizontal asymptote
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